Bài tập hệ phương trình Giải các hệ phương trình sau :
1, + + = −
−
+ = −
2 2
1
6
x xy y
MTCN
+ =
5
( 98) 13
x y
NT
x x y y
3, + =
−
+ =
30 ( 93) 35
x y y x
BK
+ =
1
( 97)
x y
AN
5, + + =
−
7 ( 1 2000) 21
x y xy
SP
+ + =
−
2 2
11
( 2000) 3( ) 28
x y xy
QG
7,
−
7 1 ( 99) 78
x xy y xy
8,
2 2 2 2
1 ( )(1 ) 5
( 99) 1
x y
xy
NT
x y
x y
9,
+ + + =
+ + + =
2 2 2 2
1 1
4 ( 99)
1 1
4
x y
x y
AN
x y
x y
10, + + =
−
+ + =
2
( 2)(2 ) 9
( 2001)
AN
x x y
11,
+ + + + + + + + + =
+ + + − + + + + − =
( 99)
AN
12, + + =
−
+ + − =
2
(3 2 )( 1) 12
2 4 8 0
x x y x
BCVT
+ =
6 ( 1 2000)
y xy x
SP
x y x
14, + =
−
2 2 3 3
4
x y
HVQHQT
( 2000)
x x y
QG
y y x
16, = − −
= −
2
2
3
3
x x y
MTCN
+ =
+ =
1 3 2
( 99)
1 3 2
x
y x QG y
x y
18, = +
−
= +
3
3
3 8
( 98)
3 8
QG
+ =
+ =
2
2
3 2
( 2001) 3
2
x y
x TL
y x
y
20, + + − =
−
+ + − =
( 1 2000)
NN
2 2 2 2
2 3
2 3
y y x x x y
=
22, − =
−
2
3 2 16
x xy
HH TPHCM
+ = −
( 2001) 6
x y x
TM
y xy x
24, − + =
−
x xy y
HVNH TPHCM
2 ( ) 3
( § 97) ( ) 10
y x y x
M C
Bài tập phương trình -bất phương trình vô tỉ
Giải các phương trình sau:
1, x+ +3 6− =x 3 2, x+ = −9 5 2x+4
3, x+ −4 1− =x 1 2− x 4,(x−3) 10−x2 =x2− −x 12
5,3 x+ −4 3 x− =3 1 6,3 2x− +1 3 x− =1 33x+1
Trang 27, 2 x+ +2 x+ −1 x+ =1 4 8, x+2 x− −1 x−2 x− =1 2(BCVT−2000)
9, 3(2+ x− =2) 2x+ x+6(HVKTQS−01)
2x +8x+ +6 x − =1 2x+2(BK−2000)
4− +x −x + 4− −x −x = +x PCCC−
( 1) ( 2) 2 ( 2 2000 )
x x− + x x+ = x SP − A
13, 2x2+8x+ +6 x2 − =1 2x+2(HVKTQS−99)
Tìm m để phương trình :
14, x2+mx+ =2 2x+1 có 2 nghiệm phân biệt
15, 2x2+mx = −3 x SPKT TPHCM( − ) có nghiệm
16, 2x2+mx− = −3 x m GT( −98) có nghiệm
Giải các phương trình sau :
17,x2 + x2+11 31= 18,(x+5)(2− =x) 3 x2+3x
x − x+ + x − x+ = TM− 20,2x2+5x− =1 7 x3−1
21,x2 +2x+ =4 3 x3+4x 22, 3− +x x2 − 2+ −x x2 =1(NT−99)
23, x+ +1 4− +x (x+1)(4−x NN)( −20001)
24,x+ 4−x2 = +2 3x 4−x2
25, x− +2 4− =x x2−6x+11
26, 2x− +3 5 2− x +4x x− − =2 6 0(GTVT TPHCM− −01)
3x− +2 x− =1 4x− +9 2 3x −5x+2(HVKTQS−97)
28,
4 2
x x
+ + =
+ 29,3 3
2( 95)
1 2 2
+
1
x
x
x
− 31, 1+ 1−x2 =x(1 2 1+ −x2) 32,(4x−1) x2+ =1 2x2 +2x+1
33,x2 +3x+ = +1 (x 3) x2+1(GT−01) 34,2(1−x x) 2+2x− =1 x2−2x−1
35, 2
1 1( 98)
x + x+ = XD− 36,32− = −x 1 x−1(TCKT−2000)
37,3 x+ −7 x =1 38,
6
x x
x
x x
− − − = −
− + − 39,
3 1 2 23 1
x + = x− Giải các bất phương trình sau :
1, (x−1)(4−x)> −x 2 2, x+ > −1 3 x+4(BK−99)
3, x+ ≥3 2x− +8 7−x AN( −97) 4, x+ −2 3− <x 5 2 (− x TL−2000)
5,(x−3) x2− ≤4 x2−9 6,1 1 4x2 3( 98)
NN x
− − < − 7,
2
(1 1)
+ + 8,
9, x2+3x+ +2 x2+6x+ ≤5 2x2+9x+7(BK−2000)
10, x2−4x+ −3 2x2−3x+ ≥ −1 x 1(KT−2001)
11, 5x2+10x+ ≥ − −1 7 x2 2x 12, −4 (4−x)(2+x)≤x2−2x−12
13,(x3+ +1) (x2+ +1) 3x x+ >1 0(XD−99)
14, 3 3 2 1 7
2 2
x x
+ < + −
15, x x( −4) − +x2 4x + −(x 2)2 <2(HVNH−99)